The cricothyroid ligament (also known as the cricothyroid membrane or Cricovocal membrane ) is composed of two parts:

the median cricothyroid ligament along the midline (a thickening of the cricothyroid membrane) and

the lateral cricothyroid ligaments on each side (these are also called conus elasticus).

The median cricothyroid ligament is a flat band of white connective tissue that connects the front parts of the contiguous margins of the cricoid and thyroid cartilages. It is a thick and strong ligament, narrow above and broad below. Each lateral ligament is known as the conus elasticus.

The conus elasticus (which means elastic cone in Latin) is the lateral portion of the cricothyroid ligament.
The lateral portions are thinner and lie close under the mucous membrane of the larynx; they extend from the upper border of the cricoid cartilage to the lower margin of the vocal ligaments, with which they are continuous. The vocal ligaments may therefore be regarded as the free borders of each conus elasticus, and extend from the vocal processes of the arytenoid cartilages to the angle of the thyroid cartilage about midway between its upper and lower borders.

These anatomical structure have been called in many different ways in the past, thus generating confusion.